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A=x^4+6x^3+7x^2–6x+1=x^4+(6x^3–2x^2)+(9x^2–6x+1)
= x^4+2x^2(3x–1)+(3x–1)^2 =(x^2+3x–1)^2
chỉnh lại tí
Đặt P(x)=x4+6x3+7x2- 6x+1
Đặt y=x2-1
=>y2=x4-2x2+1
P(x)=x4-2x2+1+6x3-6x+9x2
=(x2-1)2+6x(x2-1)+9x2
Q(y)=y2+6xy+9x2
=(y+3x)2
P(x)=(x2-1+3x)2
a) Ta có : 6x2 - 13x + 6 = 6x2 - 9x - 4x + 6 = 3x(2x - 3) - 2(2x - 3) = (3x - 2)(2x - 3)
b) Ta có: 6x2 + 7x - 3 = 6x2 + 9x - 2x - 3 = 3x(2x + 3) - (2x + 3) = (3x - 1)(2x + 3)
\(a,6x^2-13x+6\)
\(=6x^2-9x-4x+6\)
\(=3x\cdot\left(2x-3\right)-x\cdot\left(2x-3\right)\)
\(=\left(2x-3\right)\cdot\left(3x-x\right)\)
\(=\left(2x-3\right)\cdot2x\)
\(b,6x^2+7x-3\)
\(=6x^2-2x+9x-3\)
\(=2x\cdot\left(3x-1\right)+3\cdot\left(3x-1\right)\)
\(=\left(3x-1\right)\cdot\left(2x+3\right)\)
a,\(=x^3-x^2+5x^2-5x-24x+24\)
\(=x^2\left(x-1\right)+5x\left(x-1\right)-24\left(x-1\right)\)
\(=\left(x-1\right)\left(x^2+5x-24\right)\)
\(=\left(x-1\right)\left(x^2-3x+8x-24\right)\)
\(=\left(x-1\right)\left(x\left(x-3\right)+8\left(x-3\right)\right)\)
\(=\left(x-1\right)\left(x-3\right)\left(x+8\right)\)
\(x^4+3x^2+36\)
\(=\left(x^2\right)^2+2.x^2.6+6^2-9x^2\)
\(=\left(x^2+6\right)^2-\left(3x\right)^2=\left(x^2-3x+6\right)\left(x^2+3x+6\right)\)
\(2x^4-3x^3-7x^2+6x+8\)
\(=2x^4+2x^3-5x^3-5x^2-2x^2-2x+8x+8\)
\(=2x^3\left(x+1\right)-5x^2\left(x+1\right)-2x\left(x+1\right)+8\left(x+1\right)\)
\(=\left(x+1\right)\left(2x^3-5x^2-2x+8\right)\)
\(=\left(x+1\right)\left[2x^2\left(x-2\right)-x\left(x-2\right)-4\left(x-2\right)\right]\)
\(=\left(x+1\right)\left(x-2\right)\left(2x^2-x-4\right)\)
Chúc bạn học tốt.
Tìm x
x3-x2-14x+24=0
<=> x3-3x2+2x2-6x-8x+24=0
<=> x2(x-3)+2x(x-3)-8(x-3)=0
<=> (x-3)(x2+2x-8)=0
<=> (x-3)(x2-2x+4x-8)=0
<=>(x-3)(x-2)(x+4)=0
<=> x-3=0 hay x-2=0 hay x+4=0
<=> x=3 hay x=2 hay x=-4
S={3;2;-4}
\(=\left(x+1\right)\left(x-2\right)\left(2x^2-x-4\right)\)
\(6x^2+xy-7x-2y^2+7y-5=-\left(y-2x-1\right)\left(2y+3x-5\right)\)
Trả lời:
\(6x^2+xy-7x-2y^2+7y-5=-\left(y-2x-1\right)\left(2y+3x-5\right)\)
Hok_tốt nha
\(6x^2-7x-20\)
\(=6x^2+8x-15x-20\)
\(=2x\cdot\left(3x+4\right)-5\left(3x+4\right)\)
\(=\left(3x+4\right)\left(2x-5\right)\)